1. Gilberto plants 2 trees in his front yard the apple tree is 3 feet tall and will grow 20 percent each day the olive tree is two feet tall and will grow 30 percent taller each year create an equation that models each tree's height per year how many years will it take for the trees to reach the same height. 5 years 7 years 42 years 8 years
Let x be the number of years.
For the apple tree: Height = 3(1 + 0.20)^x
For the olive tree: Height = 2(1 + 0.30)^x
To find when the trees will reach the same height, we set the two equations equal to each other:
3(1 + 0.20)^x = 2(1 + 0.30)^x
Solving for x, we get:
3(1.20)^x = 2(1.30)^x
3(1.20/1.30)^x = 2
3(0.923)^x = 2
Taking the natural log on both sides:
ln (3(0.923)^x) = ln 2
ln 3 + x ln 0.923 = ln 2
x ln 0.923 = ln 2 - ln 3
x ln 0.923 = ln (2/3)
x = ln(2/3) / ln(0.923)
x ≈ 7.92 years
Therefore, it will take approximately 8 years for the two trees to reach the same height.